Inconvenient Pairs

题意翻译

给一个平面直角坐标系以及若干条平行于$x$轴或$y$轴的直线，再给出若干个在某条直线上的点（**可以在一条平行于$x$轴的直线上，也可以在一条平行于$y$轴的直线上，还可以在一条平行于$x$轴的直线与一条平行于$y$轴的直线的交点上**），求出两点间只走直线距离大于其曼哈顿距离的点对数。

题目描述

There is a city that can be represented as a square grid with corner points in $ (0, 0) $ and $ (10^6, 10^6) $ . The city has $ n $ vertical and $ m $ horizontal streets that goes across the whole city, i. e. the $ i $ -th vertical streets goes from $ (x_i, 0) $ to $ (x_i, 10^6) $ and the $ j $ -th horizontal street goes from $ (0, y_j) $ to $ (10^6, y_j) $ . All streets are bidirectional. Borders of the city are streets as well. There are $ k $ persons staying on the streets: the $ p $ -th person at point $ (x_p, y_p) $ (so either $ x_p $ equal to some $ x_i $ or $ y_p $ equal to some $ y_j $ , or both). Let's say that a pair of persons form an inconvenient pair if the shortest path from one person to another going only by streets is strictly greater than the Manhattan distance between them. Calculate the number of inconvenient pairs of persons (pairs $ (x, y) $ and $ (y, x) $ are the same pair). Let's recall that Manhattan distance between points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ |x_1 - x_2| + |y_1 - y_2| $ .

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. The first line of each test case contains three integers $ n $ , $ m $ and $ k $ ( $ 2 \le n, m \le 2 \cdot 10^5 $ ; $ 2 \le k \le 3 \cdot 10^5 $ ) — the number of vertical and horizontal streets and the number of persons. The second line of each test case contains $ n $ integers $ x_1, x_2, \dots, x_n $ ( $ 0 = x_1 < x_2 < \dots < x_{n - 1} < x_n = 10^6 $ ) — the $ x $ -coordinates of vertical streets. The third line contains $ m $ integers $ y_1, y_2, \dots, y_m $ ( $ 0 = y_1 < y_2 < \dots < y_{m - 1} < y_m = 10^6 $ ) — the $ y $ -coordinates of horizontal streets. Next $ k $ lines contains description of people. The $ p $ -th line contains two integers $ x_p $ and $ y_p $ ( $ 0 \le x_p, y_p \le 10^6 $ ; $ x_p \in \{x_1, \dots, x_n\} $ or $ y_p \in \{y_1, \dots, y_m\} $ ) — the coordinates of the $ p $ -th person. All points are distinct. It guaranteed that sum of $ n $ doesn't exceed $ 2 \cdot 10^5 $ , sum of $ m $ doesn't exceed $ 2 \cdot 10^5 $ and sum of $ k $ doesn't exceed $ 3 \cdot 10^5 $ .

输出格式

For each test case, print the number of inconvenient pairs.

输入输出样例

输入样例 #1

2
2 2 4
0 1000000
0 1000000
1 0
1000000 1
999999 1000000
0 999999
5 4 9
0 1 2 6 1000000
0 4 8 1000000
4 4
2 5
2 2
6 3
1000000 1
3 8
5 8
8 8
6 8

输出样例 #1

2
5

说明

The second test case is pictured below: For example, points $ 3 $ and $ 4 $ form an inconvenient pair, since the shortest path between them (shown red and equal to $ 7 $ ) is greater than its Manhattan distance (equal to $ 5 $ ). Points $ 3 $ and $ 5 $ also form an inconvenient pair: the shortest path equal to $ 1000001 $ (shown green) is greater than the Manhattan distance equal to $ 999999 $ . But points $ 5 $ and $ 9 $ don't form an inconvenient pair, since the shortest path (shown purple) is equal to its Manhattan distance.